Nonparametric Quantile Regression Estimation with Mixed Discrete and Continuous Data

Degui Li; Qi Li; Zheng Li

doi:10.1080/07350015.2020.1730856

Nonparametric Quantile Regression Estimation with Mixed Discrete and Continuous Data

Degui Li, Qi Li, Zheng Li

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we investigate the problem of nonparametrically estimating a conditional quantile function with mixed discrete and continuous covariates. A local linear smoothing technique combining both continuous and discrete kernel functions is introduced to estimate the conditional quantile function. We propose using a fully data-driven cross-validation approach to choose the bandwidths, and further derive the asymptotic optimality theory. In addition, we also establish the asymptotic distribution and uniform consistency (with convergence rates) for the local linear conditional quantile estimators with the data-dependent optimal bandwidths. Simulations show that the proposed approach compares well with some existing methods. Finally, an empirical application with the data taken from the IMDb website is presented to analyze the relationship between box office revenues and online rating scores.

Original language	English
Pages (from-to)	741–756
Number of pages	16
Journal	Journal of Business and Economic Statistics
Volume	39
Issue number	3
Early online date	16 Mar 2020
DOIs	https://doi.org/10.1080/07350015.2020.1730856
Publication status	Published - Jun 2021

Bibliographical note

© 2020 American Statistical Association. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

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10.1080/07350015.2020.1730856

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© 2020 American Statistical Association. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.
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Cite this

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abstract = "In this paper, we investigate the problem of nonparametrically estimating a conditional quantile function with mixed discrete and continuous covariates. A local linear smoothing technique combining both continuous and discrete kernel functions is introduced to estimate the conditional quantile function. We propose using a fully data-driven cross-validation approach to choose the bandwidths, and further derive the asymptotic optimality theory. In addition, we also establish the asymptotic distribution and uniform consistency (with convergence rates) for the local linear conditional quantile estimators with the data-dependent optimal bandwidths. Simulations show that the proposed approach compares well with some existing methods. Finally, an empirical application with the data taken from the IMDb website is presented to analyze the relationship between box office revenues and online rating scores.",

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